According to an article in the New Scientist - issue 2213, 20 November 1999, page 50 (can be found online at:
http://environment.newscientist.com/article/mg 16422135.100-king-of-hearts.html), when the sea iguana of the Galapagos Islands is in danger, as when a shark approaches, it completely changes colour and stops its heart, so the shark can't hear it. It seems that a shark can hear the heartbeat when it's three or four metres away, but its vision is very poor. Consequently, this strange adaptation would make good sense.
Apparently though, one other animal can voluntarily stop its own heart � the komodo dragon. In this case, the komodo is pretty much the top predator in its natural habitat, so under what circumstances would it need to be able to stop its heart?
A naturalist told me that he thought that neither animal could do such a thing, but the New Scientist is a pretty prestigious magazine. I would love to know the truth about this.